Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants

This paper investigates causal effect identification in latent variable Linear Non-Gaussian Acyclic Models (lvLiNGAM) using higher-order cumulants, addressing two prominent setups that are challenging in the presence of latent confounding: (1) a single proxy variable that may causally influence the treatment and (2) underspecified instrumental variable cases where fewer instruments exist than treatments. We prove that causal effects are identifiable with a single proxy or instrument and provide corresponding estimation methods. Experimental results demonstrate the accuracy and robustness of our approaches compared to existing methods, advancing the theoretical and practical understanding of causal inference in linear systems with latent confounders.

Understanding cause and effect is crucial in science and decision-making, but it's extremely difficult when some important variables are unmeasured. This is especially true in complex systems, like healthcare or economics, where data often misses key factors. Our research focuses on a class of models called Linear Non-Gaussian Acyclic Models (LiNGAM), which are commonly used to uncover causal relationships from data. A major challenge arises when only a limited number of "proxy" or "instrumental" variables are available to help identify these hidden causes. We show that even in these tough situations, it's still possible to reliably estimate causal effects. Our approach uses higher sample moments of the observed data to uncover these effects. We back our theory with experiments that show our method outperforms existing techniques in both accuracy and robustness. By improving how we handle hidden factors, our work helps move causal inference from idealized settings closer to real-world applications.